Computing with Cognitive States

TL;DR

This paper introduces an algebraic model of human working memory using high-dimensional binary states and two operations, capturing serial order effects and matching empirical data on memory tasks.

Contribution

It proposes a novel algebraic framework for cognitive states that accounts for serial order and memory gradients, differing from traditional vector symbolic architectures.

Findings

Model reproduces serial position curves observed in memory tasks

Quantitative predictions align with empirical working memory data

Highlights non-associative bundling's role in sequence preservation

Abstract

Basic experimental findings about human working memory can be described by an algebra built on high-dimensional binary states, representing information items, and two operations: multiplication for binding and addition for bundling. In contrast to common VSA algebras, bundling is not associative. Consequently bundling a sequence of items preserves their sequential ordering. The cognitive states representing a memorised list exhibit a primacy as well as a recency gradient. The typical concave-up and asymmetrically shaped serial position curve is derived as a linear combination of those gradients. Quantitative implications of the algebra are shown to agree well with empirical data from basic cognitive tasks including storage and retrieval of information in human working memory.